Energy Levels

Q. In hydrogen atom, if the difference in the energy of the electron in $n=2$ and $n=3$ orbits is $E.$, then ionization energy of hydrogen atom is $3.6nE.$ The value of $n$ is (integer only)

Q.

The transition from the state n = 4 to n = 3 in a hydrogen-like atom results in ultra violet radiation. Infrared radiation will be obtained in the transition. (IIT-JEE-2001)

1. $2\to 1$
2. $5\to 4$
3. $4\to 2$
4. $3\to 2$

Q. The wave number of energy emitted when electron jumps from fourth orbit to second orbit in hydrogen in 20497 $c{m}^{-1}$. The wave number of energy for the same transition in $H{e}^{+}$ is

1. $20,497c{m}^{-1}$
2. $5,099c{m}^{-1}$
3. $40,994c{m}^{-1}$
   
4. $81,988c{m}^{-1}$

Q. A stationary hydrogen atom emits a photon corresponding to first line of Lyman series. The velocity of recoil of the atom is

1. 3.2 m/s
2. 5.32 m/s
3. 2.79 m/s
4. 7.29 m/s

Q. Let ${\vartheta }_1$ be the frequency of the series limit of the Lyman series and ${\vartheta }_2$ be the frequency of the first line of the Lyman series ${\vartheta }_3$ be the frequency of the series limit of Balmar series, then

1. ${\vartheta }_1={\vartheta }_2-{\vartheta }_3$
2. ${\vartheta }_1–{\vartheta }_2={\vartheta }_3$
   
3. ${\vartheta }_2-{\vartheta }_1={\vartheta }_3$
   
4. $2{\vartheta }_3={\vartheta }_1+{\vartheta }_2$
   

Q. A hydrogen atom in the ground state emits a photon of energy 12.1 eV. Its orbital angular momentum changes by $\Delta$L. Then $\Delta$L is equal to

1. $1.05\times {10}^{-34}Js$
2. $2.11\times {10}^{-34}Js$
3. $3.16\times {10}^{-34}Js$
4. $4.22\times {10}^{-34}Js$

Q. Hydrogen atom emits blue light when it jumps from n = 4 energy level to the n = 2 level. Which colour of light would the atom emit when it changes from the n = 5 level to the n = 2 level?

1. Red
2. Violet
3. Green
4. Yellow

Q. The transition from the state n = 4 to n = 3 in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from :

1. $3\to 2$
2. $4\to 2$
3. $5\to 4$
4. $2\to 1$

Q. If the wavelength of first member of Balmer series of hydrogen spectrum is $6564\dot{A}$, the wavelength of second member of Balmer series will be:

1. $5892\dot{A}$
2. $1215\dot{A}$
3. $4862\dot{A}$
4. $6050\dot{A}$

Q. Energy levels A, B, C of an atom are shown below


If $E_A<E_B<E_C$, the wavelength emitted due to transistion from C to A is ${\lambda }_3$then correct statements of the following is

1. ${\lambda }_3={\lambda }_1+{\lambda }_2$
2. ${\lambda }_3=\frac{{\lambda }_1\times {\lambda }_2}{{\lambda }_2+{\lambda }_1}$
3. ${\lambda }_1+{\lambda }_2+{\lambda }_3=0$
4. ${\lambda }_3^2={\lambda }_1^2+{\lambda }_2^2$